FIG. 1 shows a sketch of a prior art interferometer. The particular interferometer shown in FIG. 1 is conventionally called a Michelson interferometer, and has been used since the nineteenth century in optical experiments and measurements. A light source 10 produces light which is collimated by passing through a lens system 11 to produce a parallel beam of light 12 which passes to a beamsplitter 13. The beam of light 12 is partially reflected to a reference mirror 14 and partially transmitted to an object 15. Light reflected from the reference mirror 14 partially passes through the beamsplitter to an image receiver 16. Light reflected from the object is partially reflected from the beamsplitter 15 and is passed to the image receiver 16. The image receiver 16 may be film, or may be an electronic photodetector or CCD or CMOS array.
If both the reference mirror 14 and the object 15 are flat mirrors aligned perpendicular to the incoming light from beam 12, and the light path traversed by the light from the light source to the image receiver is identical, the light from both the reference mirror and the object mirror will be in phase, and the image receiver will show a uniformly bright image. Such devices were the bane of undergraduate optics students before the advent of lasers, since the distances had to be equal to within a small part of the wavelength of light and the mirrors had to be aligned within microradians. Even with the advent of lasers, such devices are subject to vibration, thermal drift of dimensions, shocks, etc.
However, the Michelson interferometer design of FIG. 1 is useful to explain the many different types of interferometers known in the art. In particular, suppose the reference mirror 14 is moved back and forth in the direction of the arrow in FIG. 1. As the reference mirror is moved, the phase of the light beam reflected from the reference mirror and measured at the image receiver 16 will change by 180 degrees with respect to the phase of the light reflected from the object 15 for every displacement of one quarter wavelength. The light from the two beams reflected from the object 15 and the reference mirror 14 will interfere constructively and destructively as the mirror moves through one-quarter wavelength intervals. If the intensity on both the reference and object beam is equal, the intensity at the image receiver will be zero when the mirrors are positioned for maximum destructive interference. Very tiny displacements of one of the mirrors 14 or 15 can thus be measured.
FIG. 2 shows a sketch of an interferometer much like the interferometer of FIG. 1, except that diffusely reflecting objects 25 can be imaged on the image receiver 16 by using an additional lens 20. FIG. 2 shows also the problem solved by the method of the present invention, where the object 25 which is to be measured has a surface which is bigger than the field of view of the imaging optics.
Another inspection technique that is very useful is when the Michelson interferometer of FIG. 1 or FIG. 2 is used to compare the flatness of the surface of object 15 with the flatness of the reference mirror. As noted, if there is a difference in distance between the object mirror and the corresponding part of the reference mirror, the light from the two beams will interfere constructively or destructively and produce a pattern in the image receiver. Such patterns are generally called fringe patterns or interferograms, and can be likened to the lines on a topographic map. Such lines, as on a topographic map, can be interpreted as slopes, hills and depressions; the lines are separated in “height” by a half wavelength of the light from the light source 10.
One problem with the above inspection technique is that there are no numbers telling the difference between a depression and a hill, or in which direction the slope runs. However, if the reference mirror is moved, the lines will move, and, for example, the circles on a hill will shrink and a depression will expand for a particular direction of travel.
Interferometric techniques work very well for optical surface inspection to check whether the surface is flat, or curved to within a certain specification. However, for many surfaces which are rough on the scale of the wavelength of visible light, or have height variations or steep slopes, the “lines” of equal phase (or height) of the interferogram will be very close together. Any disturbances, noise, or other variation will make it difficult or impossible to “count” the fringes and thus measure the “height” of the various features. As an analogy, the result would be like trying to hike using a topographic map with lines every inch in height difference.
U.S. Pat. Nos. 5,907,404 and 5,926,277, assigned to the assignee of the present invention, show that a number of such interferograms taken with various phase delays in the reference beam and various wavelengths of the light source 10 may be recorded and computer analyzed to construct a “synthetic interferogram”, which is an interferogram that one would measure if one had a light source of much different wavelength from the wavelengths from the light source 10. Thus, the “lines” on the interferogram could show height differences of, say, 100 microns instead of 0.4 micron height differences, so the lines would be much further apart and much easier to keep track of. Lasers of 200 micron wavelength are hard to find, and electronic imaging equipment for such wavelengths is even harder to find, and spatial resolution of such a detector, if available, could not possibly match the resolution of detectors for visible and near infra-red light.
FIG. 3 shows the intensity recorded for a single pixel of the imaging device 16 as the reference mirror 14 is moved in steps perpendicular to the incident beam. The step distances can be converted to a phase shift of the reference beam measured at the image receiver 16. In a perfect world, the measurements would lie on a sinusoidal curve. If the intensity of the beams received from the object and the reference mirror were equal, the intensity would be zero when the two beams interfered destructively. For the usual case that the intensities in the two beams are not equal, the intensity of the interfering beams never reaches zero, and varies with an amplitude A about an average intensity IO which is related to the reflectivity of the object. The phase of the object beam at one pixel can be measured with respect to the phase at another pixel by inspecting the data shown by FIG. 3 for each pixel.
Manual inspection of results from a megapixel imaging device of course is difficult for humans, but easy for a computer programmed with a fast Fourier transform (FFT) program or other statistical analysis program. The FFT of a perfect sine wave gives a delta function telling the frequency of the wave, and in the case of a sine wave displaced from the origin also gives a “phase”, as well as the amplitude A and average intensity IO. Since the “frequency” of the results from all the pixels is the same, the relative “phase” for each pixel can be recorded from sufficient measurements of pixel intensity as the reference mirror is moved to change the phase of the reference beam. The multiple measurements remove much of the “noise” which would complicate the interpretation of an interferogram taken with an object fixed with respect to the reference mirror, as the maximum height peak of the FFT is easily identified and lower height peaks introduced by noise are ignored. The recorded measurements of phase and amplitude are sometimes called a digital hologram. The phase, amplitude, or other measurements so recorded as images are called, for the purposes of this specification, as synthetic “phase images”, and can be printed out as a two dimensional image where brightness or color is directly related to phase, intensity, etc. IO can be printed out, and looks similar to the image which would be recorded in absence of the reference beam or a normal photographic or digital image of the object.
When the field of view of the optical system is too small to “see” the entire surface of the object 25, one could translate the object a known distance in a known direction perpendicular to the object beam, and record a new interferogram, and combine the interferograms. Unfortunately, systems to hold and transport objects macroscopic distances, and place them within a small part of a wavelength in position without introducing errors and microradian tilts are extremely expensive and delicate.